Why do my sugarpaste flowers and butterflies go soft when put onto cakes? How long should I leave them to go really hard?

I always give mine at least 24 hours to dry.

could you be putting them on buttercream while they are still soft thus absorbing moisture from the buttercream? Just a thought though if you are putting them on fondant covered cake, I don't know, sorry

It all depends on your recipe. The amount of tylose in it. Also the weather has a lot to do with it also. If its humid then their going to stay softer for a longer period of time. I try to give things atleast a week to dry depending on the thickness of the paste. Flowers and butterflys can be a day or two.
You can also use silicone around them to keep the moisture away. You can get it when you purchase shoes. Its in little packets inside the shoebox. And sometimes pepperoni has it. You can also go to creative cutters online and Geraldine sells a product specific for moisture and keeping it away from your cakes. Its called desiccant. Its reuseable after you stick it in an oven. Works great and food safe (silicone is also, by the way).